SOLUTION
Use collections.Counter:
from collections import Counter
original_list = [['a', 1], ['b', 1], ['a', 1], ['b', 1], ['b', 2], ['c', 2], ['b', 3]]
result = Counter()
for k, v in original_list:
     result.update({k:v})
map(list, result.items())
# [['a', 2], ['c', 2], ['b', 7]]
FINDINGS
So, lot of answers, views and upvotes. I even earned my first Nice answer out of nothing (in last 2 days I made lot of answers worth of more research and efforts). In view of this, I decided to do at least some research and test solutions performance with a simple script written from scratch. Do not include code directly in answer for the sake of size.
Each function is named for it's author an easily can be found in question.  thefourtheye's solution now equals one of Mark Reed and is evaluated in original form, thefourtheye2 states for itertools.groupby based solution.
Each was tested several times (samples), each sample in turn invoked several function iterations. I evaluated min, max and standard deviation for samples times.
Here we go, running probing test for 10 times.
testing: thefourtheye, kroolik2, void, kroolik, alko, reed, visser
   10 samples
   10 iterations each
         author   min     avg     max    stddev
           reed 0.00000 0.00000 0.00000 0.00000
         visser 0.00000 0.00150 0.01500 0.00450
   thefourtheye 0.00000 0.00160 0.01600 0.00480
  thefourtheye2 0.00000 0.00310 0.01600 0.00620
           alko 0.00000 0.00630 0.01600 0.00772
           void 0.01500 0.01540 0.01600 0.00049
       kroolik2 0.04700 0.06430 0.07800 0.00831
        kroolik 0.32800 0.34380 0.37500 0.01716
Look at bottom two rows: at this point kroolik solutions were disqualified since with it any reasonable amount of samples*iterations will be performed for hours. Here goes final tests. I manually added number of upvotes to ouptut:
testing: thefourtheye, kroolik2, void, kroolik, alko, reed, visser
   100 samples
  1000 iterations each
         author  upvotes   min     avg     max    stddev
           reed  [20]    0.06200 0.08174 0.15600 0.01841
   thefourtheye   [5]    0.06200 0.09971 0.20300 0.01911
         visser   [6]    0.10900 0.12392 0.23500 0.02263
  thefourtheye2          0.25000 0.29674 0.89000 0.07183
           alko  [11]    0.56200 0.62309 1.04700 0.08438
           void   [3]    1.50000 1.65480 2.39100 0.18721
        kroolik  [14]     [DSQ]